{"id":"vidhyamitra:city-day:mathura:-3137-10-20:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3137-10-20","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3137-10-20","date_display":"October 20, 3138 BCE","panchanga":{"method":"Sūrya Siddhānta + Bhāskara-II iterative manda + Kerala-school (Mādhava-Nīlakaṇṭha) evection + variation + annual equation","engine_version":"2.0 (Kerala-school enhanced)","accuracy_note":"Not independently benchmarked across the declared range","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":-3137,"month":10,"day":20,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":575560.770833,"kali_year":-35,"ahargana":-12904.7292,"sun":{"sidereal_longitude":240.3871,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":239.1947,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":30,"name":"Amāvasyā","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Amāvasyā","elongation_degrees":358.8076,"elapsed_within_tithi_degrees":10.8076},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":4,"moon_longitude":239.1947,"elapsed_within_degrees":12.5281},"yoga":{"number":9,"name":"Śūla","sum_longitude":119.5818},"karana":{"half_tithi_index":59,"name":"Nāga"},"vara":{"number":3,"name":"Somavāra (Monday)"}},"sky":{"method":"Sūrya-Siddhāntic Bhāskara-II 4-step iteration with atan2-based śīghra + varying peripheries + lunar latitude","engine_version":"3.0 (Pūrṇa — complete SS implementation)","tradition_sources":"Āryabhaṭīya 499 CE → SS Ch.1-5 Burgess 1860 → Siddhānta-Śiromaṇi Bhāskara II 1150 → Tantrasaṅgraha Nīlakaṇṭha 1501","input":{"year":-3137,"month":10,"day":20,"hour":6,"minute":30,"calendar":"julian"},"julian_day":575560.770833,"ahargana":-12904.7292,"kali_year":-35,"ayanamsa_lahiri":-47.8964,"grahas":{"sun":{"sidereal_longitude":240.3871,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":1},"retrograde":false},"moon":{"sidereal_longitude":239.1947,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":4},"retrograde":false,"latitude":4.4797},"mars":{"sidereal_longitude":117.3295,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Āśleṣā","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":219.8624,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","pada":2},"retrograde":false},"jupiter":{"sidereal_longitude":0.0027,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":1,"name":"Aśvinī","pada":1},"retrograde":true},"venus":{"sidereal_longitude":225.4385,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":277.9308,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":4},"retrograde":false},"rahu":{"sidereal_longitude":143.7547,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":11,"name":"Pūrva Phalgunī","pada":4},"retrograde":false},"ketu":{"sidereal_longitude":323.7547,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":2},"retrograde":false}},"panchang":{"method":"Sūrya Siddhānta + Bhāskara-II iterative manda + Kerala-school (Mādhava-Nīlakaṇṭha) evection + variation + annual equation","engine_version":"2.0 (Kerala-school enhanced)","accuracy_note":"Not independently benchmarked across the declared range","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":-3137,"month":10,"day":20,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":575560.770833,"kali_year":-35,"ahargana":-12904.7292,"sun":{"sidereal_longitude":240.3871,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":239.1947,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":30,"name":"Amāvasyā","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Amāvasyā","elongation_degrees":358.8076,"elapsed_within_tithi_degrees":10.8076},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":4,"moon_longitude":239.1947,"elapsed_within_degrees":12.5281},"yoga":{"number":9,"name":"Śūla","sum_longitude":119.5818},"karana":{"half_tithi_index":59,"name":"Nāga"},"vara":{"number":3,"name":"Somavāra (Monday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":4.48,"elongation":1.192},"lunar":{"type":"lunar","occurs":false,"moon_latitude":4.48,"opposition_distance":178.808}},"eclipse_window_40days":[]},"city":{"slug":"mathura","name":"Mathurā","lat":27.4924,"lon":77.6737,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"tier2":{"city":{"slug":"mathura","name":"Mathurā","lat":27.4924,"lon":77.6737,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"sunriseLocal":"06:10","sunsetLocal":"17:57","solarNoonLocal":"12:04","dayLengthHours":11.782380499863251,"dayLengthDisplay":"11 Hours 46 Mins 57 Secs","nightLengthDisplay":"12 Hours 13 Mins 03 Secs","moonriseLocal":"06:06","moonsetLocal":"17:52","rahuKala":{"name":"Rāhu Kāla","start":"07:39","end":"09:07","startHours":7.641746125147427,"endHours":9.114543687630334,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"10:35","end":"12:04","startHours":10.58734125011324,"endHours":12.060138812596147,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"13:32","end":"15:00","startHours":13.532936375079053,"endHours":15.00573393756196,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:55","end":"09:19","startHours":8.91817067929928,"endHours":9.310916695961387,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:40","end":"06:58","startHours":6.659881083492156,"endHours":6.974077896821843,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:40","end":"12:27","startHours":11.667392795934038,"endHours":12.452884829258256,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:36","end":"05:23","startHours":4.597964496016087,"endHours":5.383456529340304,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"05:11","end":"06:10","startHours":5.187083521009249,"endHours":6.168948562664521,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:01","end":"14:49","startHours":14.023868895906688,"endHours":14.809360929230904,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:45","end":"18:09","startHours":17.751329062527773,"endHours":18.151329062527772,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:57","end":"18:27","startHours":17.951329062527773,"endHours":18.442261583355407,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:42","end":"19:27","startHours":17.701329062527773,"endHours":19.451329062527773,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:40","end":"00:27","startHours":23.667392795934038,"endHours":24.452884829258256,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Amṛta","start":"06:10","end":"07:39","startHours":6.168948562664521,"endHours":7.641746125147427,"quality":"auspicious"},{"name":"Kāla","start":"07:39","end":"09:07","startHours":7.641746125147427,"endHours":9.114543687630334,"quality":"inauspicious"},{"name":"Śubha","start":"09:07","end":"10:35","startHours":9.114543687630334,"endHours":10.58734125011324,"quality":"auspicious"},{"name":"Roga","start":"10:35","end":"12:04","startHours":10.58734125011324,"endHours":12.060138812596147,"quality":"inauspicious"},{"name":"Udveg","start":"12:04","end":"13:32","startHours":12.060138812596147,"endHours":13.532936375079053,"quality":"inauspicious"},{"name":"Chala","start":"13:32","end":"15:00","startHours":13.532936375079053,"endHours":15.00573393756196,"quality":"neutral"},{"name":"Labha","start":"15:00","end":"16:29","startHours":15.00573393756196,"endHours":16.478531500044866,"quality":"auspicious"},{"name":"Amṛta","start":"16:29","end":"17:57","startHours":16.478531500044866,"endHours":17.951329062527773,"quality":"auspicious"}],"nightChoghadiyas":[{"name":"Chala","start":"17:57","end":"19:29","startHours":17.951329062527773,"endHours":19.478531500044866,"quality":"neutral"},{"name":"Labha","start":"19:29","end":"21:00","startHours":19.478531500044866,"endHours":21.00573393756196,"quality":"auspicious"},{"name":"Amṛta","start":"21:00","end":"22:32","startHours":21.00573393756196,"endHours":22.532936375079053,"quality":"auspicious"},{"name":"Kāla","start":"22:32","end":"00:04","startHours":22.532936375079053,"endHours":24.060138812596147,"quality":"inauspicious"},{"name":"Śubha","start":"00:04","end":"01:35","startHours":24.060138812596147,"endHours":25.58734125011324,"quality":"auspicious"},{"name":"Roga","start":"01:35","end":"03:07","startHours":25.58734125011324,"endHours":27.114543687630334,"quality":"inauspicious"},{"name":"Udveg","start":"03:07","end":"04:39","startHours":27.114543687630334,"endHours":28.641746125147428,"quality":"inauspicious"},{"name":"Chala","start":"04:39","end":"06:10","startHours":28.641746125147428,"endHours":30.16894856266452,"quality":"neutral"}],"horas":[{"name":"Hora 1","start":"06:10","end":"07:10","startHours":6.168948562664521,"endHours":7.168948562664521,"planetary_lord":"Moon"},{"name":"Hora 2","start":"07:10","end":"08:10","startHours":7.168948562664521,"endHours":8.168948562664522,"planetary_lord":"Mercury"},{"name":"Hora 3","start":"08:10","end":"09:10","startHours":8.168948562664522,"endHours":9.168948562664522,"planetary_lord":"Venus"},{"name":"Hora 4","start":"09:10","end":"10:10","startHours":9.168948562664522,"endHours":10.168948562664522,"planetary_lord":"Sun"},{"name":"Hora 5","start":"10:10","end":"11:10","startHours":10.168948562664522,"endHours":11.168948562664522,"planetary_lord":"Mars"},{"name":"Hora 6","start":"11:10","end":"12:10","startHours":11.168948562664522,"endHours":12.168948562664522,"planetary_lord":"Jupiter"},{"name":"Hora 7","start":"12:10","end":"13:10","startHours":12.168948562664522,"endHours":13.168948562664522,"planetary_lord":"Saturn"},{"name":"Hora 8","start":"13:10","end":"14:10","startHours":13.168948562664522,"endHours":14.168948562664522,"planetary_lord":"Moon"},{"name":"Hora 9","start":"14:10","end":"15:10","startHours":14.168948562664522,"endHours":15.168948562664522,"planetary_lord":"Mercury"},{"name":"Hora 10","start":"15:10","end":"16:10","startHours":15.168948562664522,"endHours":16.16894856266452,"planetary_lord":"Venus"},{"name":"Hora 11","start":"16:10","end":"17:10","startHours":16.16894856266452,"endHours":17.16894856266452,"planetary_lord":"Sun"},{"name":"Hora 12","start":"17:10","end":"18:10","startHours":17.16894856266452,"endHours":18.16894856266452,"planetary_lord":"Mars"},{"name":"Hora 13","start":"18:10","end":"19:10","startHours":18.16894856266452,"endHours":19.16894856266452,"planetary_lord":"Jupiter"},{"name":"Hora 14","start":"19:10","end":"20:10","startHours":19.16894856266452,"endHours":20.16894856266452,"planetary_lord":"Saturn"},{"name":"Hora 15","start":"20:10","end":"21:10","startHours":20.16894856266452,"endHours":21.16894856266452,"planetary_lord":"Moon"},{"name":"Hora 16","start":"21:10","end":"22:10","startHours":21.16894856266452,"endHours":22.16894856266452,"planetary_lord":"Mercury"},{"name":"Hora 17","start":"22:10","end":"23:10","startHours":22.16894856266452,"endHours":23.16894856266452,"planetary_lord":"Venus"},{"name":"Hora 18","start":"23:10","end":"00:10","startHours":23.16894856266452,"endHours":24.16894856266452,"planetary_lord":"Sun"},{"name":"Hora 19","start":"00:10","end":"01:10","startHours":24.16894856266452,"endHours":25.16894856266452,"planetary_lord":"Mars"},{"name":"Hora 20","start":"01:10","end":"02:10","startHours":25.16894856266452,"endHours":26.16894856266452,"planetary_lord":"Jupiter"},{"name":"Hora 21","start":"02:10","end":"03:10","startHours":26.16894856266452,"endHours":27.16894856266452,"planetary_lord":"Saturn"},{"name":"Hora 22","start":"03:10","end":"04:10","startHours":27.16894856266452,"endHours":28.16894856266452,"planetary_lord":"Moon"},{"name":"Hora 23","start":"04:10","end":"05:10","startHours":28.16894856266452,"endHours":29.16894856266452,"planetary_lord":"Mercury"},{"name":"Hora 24","start":"05:10","end":"06:10","startHours":29.16894856266452,"endHours":30.16894856266452,"planetary_lord":"Venus"}],"taraBala":{"favorable_nakshatras":["Aśvinī","Bharaṇī","Kṛttikā","Rohiṇī","Mṛgaśirā","Maghā","Pūrva Phalgunī","Uttara Phalgunī","Hasta","Citrā","Mūla","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā"],"unfavorable_nakshatras":["Ārdrā","Punarvasu","Puṣya","Aśleṣā","Svātī","Viśākhā","Anurādhā","Jyeṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Meṣa","Vṛṣabha","Siṃha","Kanyā","Vṛścika","Makara"],"unfavorable_rashis":["Mithuna","Karka","Tulā","Dhanu","Kumbha","Mīna"]},"dishaShool":"East (Pūrva)","chandraVasa":"North-East","rahuVasa":"North-East","anandadiYoga":{"name":"Mausala","quality":"Inauspicious"},"tropicalRitu":"Śarad (Autumn) (tropical)","vedicRitu":"Hemanta (Pre-winter)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-4.9347982262610905,"eotMinutes":15.696871244231174,"ayanamsa":-47.8964}},"calendars":{"vikram_samvat":-3080,"saka_samvat":-3215,"bengali_samvat":-3730,"malayalam_era":-3961,"nanakshahi_year":-4606,"lunar_month":"Pauṣa","lunar_month_paksha_full":"Pauṣa Kṛṣṇa Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Pauṣa","lunar_month_amanta":"Pauṣa","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Dhanus (Mārgaḻi)","ritu":"Hemanta (Pre-winter)","display_summary":"Pauṣa Kṛṣṇa Amāvasyā · Vikram -3080 undefined · Śaka -3215 undefined"},"festivals":[],"todays_walk":{"walk":{"id":"chandra-walk","name":"Candra Walk","name_sanskrit":"चन्द्र यात्रा","type":"graha","description":"Manas-control + BG 6.5-7, 6.34-35.","step_count":5,"url":"/walk/chandra-walk","steps":[{"label":"BG 6.5","url":"/bhagavad-gita/6/5","purpose":"Lift the self by the Self; begin the walk with inner responsibility."},{"label":"BG 6.6","url":"/bhagavad-gita/6/6","purpose":"See the mind as friend when mastered and enemy when unmastered."},{"label":"BG 6.7","url":"/bhagavad-gita/6/7","purpose":"Stabilize the conquered mind in heat/cold, honor/dishonor, pleasure/pain."},{"label":"BG 6.34","url":"/bhagavad-gita/6/34","purpose":"Name the restless mind honestly before trying to discipline it."},{"label":"BG 6.35","url":"/bhagavad-gita/6/35","purpose":"Complete with abhyāsa and vairāgya: practice and detachment."}]},"reason":"Somavāra (Monday) — its presiding graha's walk."},"cosmic_resonances":[]},"validity":{"eternal":true,"location_specific":"mathura"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate + Vidhyamitra Tier-2 layer"},"seo":{"title":"Pañchāṅga October 20, 3138 BCE · Mathurā · Vidhyamitra","description":"October 20, 3138 BCE for Mathurā: Kṛṣṇa Amāvasyā, sūryodaya 06:10, sūryāsta 17:57.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3137-10-20","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3137-10-20","sa":"https://sa.vidhyamitra.com/city/mathura/-3137-10-20","hi":"https://hi.vidhyamitra.com/city/mathura/-3137-10-20","x-default":"https://vidhyamitra.com/city/mathura/-3137-10-20"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-09-06T13:19:39.907Z","verification":{"type":"multi-marker","confidence":"canonical"}},{"pillar":"Vidhyamitra-Tier2","pillar_version":"0.1.0","method":"Spherical astronomy + Lahiri ayanamsa + standard solar declination + EoT correction","retrieved_at":"2026-09-06T13:19:39.907Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-09-06T13:19:39.907Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"},"reader_local_antaryami":{"reader_geography":"Every reader enters from their own kṣetra anywhere on Bhūmi; no single city is the universal center.","purna_chain":["Hosted scripture","Named-tradition interpretation","Original Vidhyamitra contemplation","Bhūmi-born material medium","Vidhyamitra portal","Responsible reader in their own kṣetra"],"claim_boundary":"The legacy purna_chain field carries a source-to-reader sequence, not a revealed physical descent, universal cosmology, or proof that software is conscious.","antaryami_responsibility_formula":"Kṣīrodakaśāyī Viṣṇu = Paramātmā = Antaryāmī. Jīva desires. Prakṛti executes through guṇas. Paramātmā witnesses, permits, remembers, guides, and sustains. Bhagavān is the ultimate source.","source_anchors":[{"label":"BG 13.23","path":"/bhagavad-gita/13/23","meaning":"upadraṣṭā-anumantā · witness-permitter"},{"label":"BG 15.15","path":"/bhagavad-gita/15/15","meaning":"the Lord seated in every heart as memory, knowledge, and forgetting"},{"label":"BG 18.61","path":"/bhagavad-gita/18/61","meaning":"Īśvara seated in the heart of all beings"}],"nama_seal":"Hare Krishna Hare Krishna · Krishna Krishna Hare Hare · Hare Rama Hare Rama · Rama Rama Hare Hare"}}}